ckw03_c |

## Procedurevoid ckw03_c ( SpiceInt handle, SpiceDouble begtim, SpiceDouble endtim, SpiceInt inst, ConstSpiceChar * ref, SpiceBoolean avflag, ConstSpiceChar * segid, SpiceInt nrec, ConstSpiceDouble sclkdp [], ConstSpiceDouble quats [][4], ConstSpiceDouble avvs [][3], SpiceInt nints, ConstSpiceDouble starts [] ) ## AbstractAdd a type 3 segment to a C-kernel. ## Required_ReadingCK DAF SCLK ## KeywordsPOINTING UTILITY ## Brief_I/OVariable I/O Description -------- --- -------------------------------------------------- handle I Handle of an open CK file. begtim I The beginning encoded SCLK of the segment. endtim I The ending encoded SCLK of the segment. inst I The NAIF instrument ID code. ref I The reference frame of the segment. avflag I True if the segment will contain angular velocity. segid I Segment identifier. nrec I Number of pointing records. sclkdp I Encoded SCLK times. quats I Quaternions representing instrument pointing. avvs I Angular velocity vectors. nints I Number of intervals. starts I Encoded SCLK interval start times. ## Detailed_Inputhandle is the handle of the CK file to which the segment will be written. The file must have been opened with write access. begtim is the beginning encoded SCLK time of the segment. This value should be less than or equal to the first time in the segment. endtim is the encoded SCLK time at which the segment ends. This value should be greater than or equal to the last time in the segment. inst is the NAIF integer ID code for the instrument. ref is a character string which specifies the reference frame of the segment. This should be one of the frames supported by the SPICELIB routine NAMFRM which is an entry point of FRAMEX. The rotation matrices represented by the quaternions that are to be written to the segment transform the components of vectors from the inertial reference frame specified by ref to components in the instrument fixed frame. Also, the components of the angular velocity vectors to be written to the segment should be given with respect to ref. ref should be the name of one of the frames supported by the SPICELIB routine NAMFRM. avflag is a boolean flag which indicates whether or not the segment will contain angular velocity. segid is the segment identifier. A CK segment identifier may contain up to 40 characters, excluding the terminating null. nrec is the number of pointing instances in the segment. sclkdp are the encoded spacecraft clock times associated with each pointing instance. These times must be strictly increasing. quats is an array of SPICE-style quaternions representing a sequence of C-matrices. See the discussion of "Quaternion Styles" in the Particulars section below. The C-matrix represented by the ith quaternion in quats is a rotation matrix that transforms the components of a vector expressed in the inertial frame specified by ref to components expressed in the instrument fixed frame at the time sclkdp[i]. Thus, if a vector V has components x, y, z in the inertial frame, then V has components x', y', z' in the instrument fixed frame where: [ x' ] [ ] [ x ] | y' | = | cmat | | y | [ z' ] [ ] [ z ] avvs are the angular velocity vectors ( optional ). The ith vector in avvs gives the angular velocity of the instrument fixed frame at time sclkdp[i]. The components of the angular velocity vectors should be given with respect to the inertial reference frame specified by ref. The direction of an angular velocity vector gives the right-handed axis about which the instrument fixed reference frame is rotating. The magnitude of the vector is the magnitude of the instantaneous velocity of the rotation, in radians per second. If avflag is FALSE then this array is ignored by the routine; however it still must be supplied as part of the calling sequence. nints is the number of intervals that the pointing instances are partitioned into. starts are the start times of each of the interpolation intervals. These times must be strictly increasing and must coincide with times for which the segment contains pointing. ## Detailed_OutputNone. See Files section. ## ParametersNone. ## Exceptions1) If handle is not the handle of a C-kernel opened for writing the error will be diagnosed by routines called by this routine. 2) If segid is more than 40 characters long, the error SPICE(SEGIDTOOLONG) is signaled. 3) If segid contains any nonprintable characters, the error SPICE(NONPRINTABLECHARS) is signaled. 4) If the first encoded SCLK time is negative then the error SPICE(INVALIDSCLKTIME) is signaled. If any subsequent times are negative the error SPICE(TIMESOUTOFORDER) is signaled. 5) If the encoded SCLK times are not strictly increasing, the error SPICE(TIMESOUTOFORDER) is signaled. 6) If begtim is greater than sclkdp[0] or endtim is less than sclkdp[nrec-1], the error SPICE(INVALIDDESCRTIME) is signaled. 7) If the name of the reference frame is not one of those supported by the SPICELIB routine NAMFRM, the error SPICE(INVALIDREFFRAME) is signaled. 8) If nrec, the number of pointing records, is less than or equal to 0, the error SPICE(INVALIDNUMRECS) is signaled. 9) If nints, the number of interpolation intervals, is less than or equal to 0, the error SPICE(INVALIDNUMINTS) is signaled. 10) If the encoded SCLK interval start times are not strictly increasing, the error SPICE(TIMESOUTOFORDER) is signaled. 11) If an interval start time does not coincide with a time for which there is an actual pointing instance in the segment, then the error SPICE(INVALIDSTARTTIME) is signaled. 12) This routine assumes that the rotation between adjacent quaternions that are stored in the same interval has a rotation angle of THETA radians, where 0 < THETA < pi. _ The routines that evaluate the data in the segment produced by this routine cannot distinguish between rotations of THETA radians, where THETA is in the interval [0, pi), and rotations of THETA + 2 * k * pi radians, where k is any integer. These `large' rotations will yield invalid results when interpolated. You must ensure that the data stored in the segment will not be subject to this sort of ambiguity. 14) If the start time of the first interval and the time of the first pointing instance are not the same, the error SPICE(TIMESDONTMATCH) is signaled. 15) If any quaternion has magnitude zero, the error SPICE(ZEROQUATERNION) is signaled. ## FilesThis routine adds a type 3 segment to a C-kernel. The C-kernel may be either a new one or an existing one opened for writing. ## ParticularsFor a detailed description of a type 3 CK segment please see the CK Required Reading. This routine relieves the user from performing the repetitive calls to the DAF routines necessary to construct a CK segment. Quaternion Styles ----------------- There are different "styles" of quaternions used in science and engineering applications. Quaternion styles are characterized by - The order of quaternion elements - The quaternion multiplication formula - The convention for associating quaternions with rotation matrices Two of the commonly used styles are - "SPICE" > Invented by Sir William Rowan Hamilton > Frequently used in mathematics and physics textbooks - "Engineering" > Widely used in aerospace engineering applications CSPICE function interfaces ALWAYS use SPICE quaternions. Quaternions of any other style must be converted to SPICE quaternions before they are passed to CSPICE functions. Relationship between SPICE and Engineering Quaternions ------------------------------------------------------ Let M be a rotation matrix such that for any vector V, M*V is the result of rotating V by theta radians in the counterclockwise direction about unit rotation axis vector A. Then the SPICE quaternions representing M are (+/-) ( cos(theta/2), sin(theta/2) A(1), sin(theta/2) A(2), sin(theta/2) A(3) ) while the engineering quaternions representing M are (+/-) ( -sin(theta/2) A(1), -sin(theta/2) A(2), -sin(theta/2) A(3), cos(theta/2) ) For both styles of quaternions, if a quaternion q represents a rotation matrix M, then -q represents M as well. Given an engineering quaternion QENG = ( q0, q1, q2, q3 ) the equivalent SPICE quaternion is QSPICE = ( q3, -q0, -q1, -q2 ) Associating SPICE Quaternions with Rotation Matrices ---------------------------------------------------- Let FROM and TO be two right-handed reference frames, for example, an inertial frame and a spacecraft-fixed frame. Let the symbols V , V FROM TO denote, respectively, an arbitrary vector expressed relative to the FROM and TO frames. Let M denote the transformation matrix that transforms vectors from frame FROM to frame TO; then V = M * V TO FROM where the expression on the right hand side represents left multiplication of the vector by the matrix. Then if the unit-length SPICE quaternion q represents M, where q = (q0, q1, q2, q3) the elements of M are derived from the elements of q as follows: +- -+ | 2 2 | | 1 - 2*( q2 + q3 ) 2*(q1*q2 - q0*q3) 2*(q1*q3 + q0*q2) | | | | | | 2 2 | M = | 2*(q1*q2 + q0*q3) 1 - 2*( q1 + q3 ) 2*(q2*q3 - q0*q1) | | | | | | 2 2 | | 2*(q1*q3 - q0*q2) 2*(q2*q3 + q0*q1) 1 - 2*( q1 + q2 ) | | | +- -+ Note that substituting the elements of -q for those of q in the right hand side leaves each element of M unchanged; this shows that if a quaternion q represents a matrix M, then so does the quaternion -q. To map the rotation matrix M to a unit quaternion, we start by decomposing the rotation matrix as a sum of symmetric and skew-symmetric parts: 2 M = [ I + (1-cos(theta)) OMEGA ] + [ sin(theta) OMEGA ] symmetric skew-symmetric OMEGA is a skew-symmetric matrix of the form +- -+ | 0 -n3 n2 | | | OMEGA = | n3 0 -n1 | | | | -n2 n1 0 | +- -+ The vector N of matrix entries (n1, n2, n3) is the rotation axis of M and theta is M's rotation angle. Note that N and theta are not unique. Let C = cos(theta/2) S = sin(theta/2) Then the unit quaternions Q corresponding to M are Q = +/- ( C, S*n1, S*n2, S*n3 ) The mappings between quaternions and the corresponding rotations are carried out by the CSPICE routines q2m_c {quaternion to matrix} m2q_c {matrix to quaternion} m2q_c always returns a quaternion with scalar part greater than or equal to zero. SPICE Quaternion Multiplication Formula --------------------------------------- Given a SPICE quaternion Q = ( q0, q1, q2, q3 ) corresponding to rotation axis A and angle theta as above, we can represent Q using "scalar + vector" notation as follows: s = q0 = cos(theta/2) v = ( q1, q2, q3 ) = sin(theta/2) * A Q = s + v Let Q1 and Q2 be SPICE quaternions with respective scalar and vector parts s1, s2 and v1, v2: Q1 = s1 + v1 Q2 = s2 + v2 We represent the dot product of v1 and v2 by <v1, v2> and the cross product of v1 and v2 by v1 x v2 Then the SPICE quaternion product is Q1*Q2 = s1*s2 - <v1,v2> + s1*v2 + s2*v1 + (v1 x v2) If Q1 and Q2 represent the rotation matrices M1 and M2 respectively, then the quaternion product Q1*Q2 represents the matrix product M1*M2 ## ExamplesThis example code fragment writes a type 3 C-kernel segment for the Mars Global Surveyor spacecraft bus to a previously opened CK file attached to HANDLE. /. Include CSPICE interface definitions. ./ #include "SpiceUsr.h" . . . /. Assume arrays of quaternions, angular velocities, and the associated SCLK times are produced elsewhere. The software that calls ## Restrictions1) The creator of the segment is given the responsibility for determining whether it is reasonable to interpolate between two given pointing values. 2) This routine assumes that the rotation between adjacent quaternions that are stored in the same interval has a rotation angle of THETA radians, where 0 < THETA < pi. _ The routines that evaluate the data in the segment produced by this routine cannot distinguish between rotations of THETA radians, where THETA is in the interval [0, pi), and rotations of THETA + 2 * k * pi radians, where k is any integer. These `large' rotations will yield invalid results when interpolated. You must ensure that the data stored in the segment will not be subject to this sort of ambiguity. 3) All pointing instances in the segment must belong to one and only one of the intervals. ## Literature_ReferencesNone. ## Author_and_InstitutionK.R. Gehringer (JPL) N.J. Bachman (JPL) J.M. Lynch (JPL) B.V. Semenov (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 2.0.0, 01-JUN-2010 (NJB) The check for non-unit quaternions has been replaced with a check for zero-length quaternions. (The implementation of the check is located in ckw03_.) -CSPICE Version 1.4.2, 27-FEB-2008 (NJB) Updated header; added information about SPICE quaternion conventions. -CSPICE Version 1.4.1, 27-SEP-2005 (BVS) Added an item for SPICE(TIMESDONTMATCH) exception to the Exceptions section of the header. -CSPICE Version 1.3.1, 07-JAN-2004 (EDW) Trivial typo correction in index entries section. -CSPICE Version 1.3.0, 28-AUG-2001 (NJB) Changed prototype: inputs sclkdp, quats, avvs, and starts are now const-qualified. Implemented interface macros for casting these inputs to const. -CSPICE Version 1.2.0, 02-SEP-1999 (NJB) Local type logical variable now used for angular velocity flag used in interface of ckw03_. -CSPICE Version 1.1.0, 08-FEB-1998 (NJB) References to C2F_CreateStr_Sig were removed; code was cleaned up accordingly. String checks are now done using the macro CHKFSTR. -CSPICE Version 1.0.0, 25-OCT-1997 (NJB) Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT) ## Index_Entrieswrite ck type_3 pointing data segment |

Wed Apr 5 17:54:30 2017